The Coalescent
Eric C. Anderson
Conservation Genomics Workshop, Monday August 26, 2024
Overview
Goal: Introduce the Coalescent and convey why it is a crucial model for understanding genetic variation
Outline:
Deriving the coalescent from the Wright-Fisher model
R-notebook interlude: the exponential and geometric distributions
Expected properties of coalescent trees
Expected interval times
Expected total branch lengths
Shapes of the coalescent under different demographic scenarios
Hands-on: simulating and visualizing coalescent trees
Mutations on the coalescent
Group activity: “Find your branch”
The site frequency spectrum
Hands-on: simulating 1-D SFS from different demographic scenarios
The Wright Fisher model
A simple model for the random process of genes getting from one generation to the next in a population
Assumptions
Population of constant size
No selection
Haploid organisms (diploids are treated) as
\(2N\)
haploids
No sexes
Next generation is obtained by sampling from replacement from amongst the gene copies of the previous generation
The Wright Fisher model. 40 diploids for 10 generations
The Wright Fisher model. Same thing, but re-ordered
The Wright Fisher model. Colored Alleles